A Bayesian Chi-Squared Test for Goodness of Fit

Valen Johnson
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Valen Johnson: University of Michigan School of Public Health

No 1000, The University of Michigan Department of Biostatistics Working Paper Series from Berkeley Electronic Press

Abstract: This article describes an extension of classical x 2 goodness-of-fit tests to Bayesian model assessment. The extension, which essentially involvesevaluating Pearson's goodness-of-fit statistic at a parameter value drawn from its posterior distribution, has the important property that it is asymptoti-cally distributed as a x2 random variable on K-1 degrees of freedom, indepen-dently of the dimension of the underlying parameter vector. By averaging over the posterior distribution of this statistic, a global goodness-of-fit diagnostic is obtained. Advantages of this diagnostic{which may be interpreted as the area under an ROC curve{include ease of interpretation, computational conve-nience, and favorable power properties. The proposed diagnostic can be used to assess the adequacy of a broad class of Bayesian models, essentially requir- ing only a finite-dimensional parameter vector and conditionally independent observations.

Keywords: model assessment; ROC analysis; Bayesian modeling; hierarchical models; contingency tables (search for similar items in EconPapers)
Date: 2004-07-11
Note: oai:bepress.com:umichbiostat-1000
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Citations: View citations in EconPapers (4)

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